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arXiv · 1101.3064

Monads with arities and their associated theories

Clemens Berger·Paul-André Melliès·Mark Weber
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Abstract

After a review of the concept of "monad with arities" we show that the category of algebras for such a monad has a canonical dense generator. This is used to extend the correspondence between finitary monads on sets and Lawvere's algebraic theories to a general correspondence between monads and theories for a given category with arities. As application we determine arities for the free groupoid monad on involutive graphs and recover the symmetric simplicial nerve characterisation of groupoids.

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Clemens Berger, Paul-André Melliès, Mark Weber. 2011-01-16. Monads with arities and their associated theories. https://doi.org/10.1016/j.jpaa.2012.02.039

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